Adaptive Monte Carlo methods for solving hyperbolic telegraph equation

Here, empirical studies with adaptive Monte Carlo and the almost optimal Monte Carlo methods for solving hyperbolic telegraph equations are discussed. Due to applying the difference discretization, a large sparse system is obtained. Adaptive Monte Carlo methods are employed to solve this large system. Illustrative examples of telegraph equation are considered to compare the power and accuracy of adaptive Monte Carlo methods. Numerical test results show that the almost optimal Monte Carlo method has much slower convergence speed, adaptive importance sampling method does not always converge faster than adaptive correlated sequential sampling method, and the advantage of adaptive correlated sequential sampling method over adaptive importance sampling and the almost optimal Monte Carlo methods, as well as some deterministic methods, is evident.